and the sum is \(*\) -strongly convergent.
This decomposition corresponds to the discrete Fourier expansion with respect
to the action \(({\hbox{\rm Ad\,}}V_{\mathrm {c}})\otimes ({\hbox{\rm Ad\,}}V_{\mathrm {c}})\)  of the group \(S^1\times S^1\) .
The group \(S^1\times S^1\)  acts also on \(\mathcal {M}_{\mathrm {c}}\otimes \mathcal {M}_{\mathrm {c}}\)  and there is a decomposition
into components as well.
For a corresponding proof, see again [1]}.
